Math Seminar: David Ayala (MSU) “G-representations are vector bundles”
- Monday, October 15, 2018 from 4:00pm to 5:00pm
- Wilson Hall, 1-144 - view map
Part 2 of 2.
The goal of this talk is to state and contextualize the following.
Let G be a compact Lie group (such as a finite group).
There is a stratified geometric object, \fB G, with one stratum for each conjugacy class of a closed subgroup H of G. This geometric object has the property that the collection of vector bundles over it is identical to that of vector spaces equipped with a linear G-action, and restriction to the [H]-stratum is implemented by taking H-fixed points.
This result is a generalization of the classification of covering spaces in terms of the fundamental group (such as in Chapter 1 of Hatcher’s book on Algebraic Topology).
There are two main consequences to this theorem. First, `cyclotomic vector spaces’ can be interpreted as vector bundles over the \fB T, where T is the circle group, that are invariant with respect to endomorphisms of T. Second, using this interpretation, there is a `cyclotomic trace map’ from vector bundles over a scheme to cyclotomic vector spaces.
- Department of Mathematical Sciences